MPA Blackboard Lectures Dragan Huterer, University of Michigan Dark Energy and the Accelerating Universe Recommended reading: \Dark Energy and the Accelerating Universe", J. Frieman, M. Turner and D. Huterer, Ann. • Rev. Astron. Astrophys. 46, 385 (2008), arXiv:0803.0982 | a 40-page review of DE for a general-practice physicist or astronomer. ∼ \Observational Probes of Cosmic Acceleration", D. Weinberg, M. Mortonson, D.J. Eisen- • stein, C. Hirata, A. Riess, and E. Rozo, Phys. Rept. 530, 87 (2013); arXiv:1201.2434 | a super-detailed, definitive review on cosmological probes of DE. \Dynamics of Dark Energy", E. Copeland, M. Sami and S. Tsujikawa, Int. J. Mod. Phys. • D15, 1753 (2006), arXiv:hep-th/0603057 | a detailed review strong on theoretical attempts to explain DE. \Measurements of the cosmological parameters ΩM and Λ from 42 high-redshift super- • novae", S. Perlmutter et al. (The Supernova Cosmology Project), Astrophysical Journal 517, 565 (1999) | a classic. \Supernovae, Dark Energy, and the Accelerating Universe", S. Perlmutter, Physics Today, • April 2003 | very nice popular account. \The Extravagant Universe", R.P. Kirshner, Princeton Univ Press 2004 | an entertaining • book about the discovery of DE. History of the discovery of DE. Type Ia Supernovae. Early signs of a new component. At least as far back as the 1980s (and probably earlier), there has emerged evidence that the matter density in the universe is low, roughly ΩM 0:1-0:3. While the precise value was hard to pin down due to various systematics, it was pretty' clear that the matter density was far from the value predicted by inflation, ΩM = 1:0. One line of argument for low ΩM used measurements of the age of the universe, which was lower-bounded to t0 & 12-15 Gyr using ages of globular clusters. In a flat, matter-dominated −1 −1 universe, the age is t0 = (2=3)H0 6:5h Gyr, where h = H0=(100 km=s=Mpc). Even for lowest values of the Hubble constant' reasonably expected at the time, h 0:5, the age is uncomfortably low. ' The other line of argument includes various probes of galaxy clustering, velocities, and struc- ture formation in general. The simplest and most compelling argument is that the measured \shape parameter" Γ ΩM h of the galaxy power spectrum, which determines the turnover that corresponds to the size≡ of the universe at matter-radiation equality, is surprisingly low. Γ 0:25 ' has consistently been measured implying, for reasonably values of the Hubble constant, that ΩM simply cannot be one. Faced with these difficulties, cosmologists have proposed all kinds of theoretical explanations in the 80s and early-to-mid 90s, including actually the cosmological constant (vacuum energy). Parallel to these developments, a group at UC Berkeley has been planning to develop strate- gies to use special property of type Ia supernovae { that of an (approximate) standard candle { in order to build the Hubble diagram and decide if the universe is open, flat or closed. Standard Candles. A \standard candle" is a hypothetical object that has a fixed luminosity (that is, fixed intrinsic power that it radiates). Having a standard candle would be useful since 1 then you could infer distances from objects just by using the inverse square law. In fact, you don't even to know the luminosity of the standard candle to be able to infer relative distances to objects. In other words, if you know that L is constant, then by measuring the flux L f = 2 (1) 4πdL you immediately get ratios of luminosity distances (but not the absolute scales unless if you actually know the value of L). Type Ia supernovae. Type Ia supernovae are interesting objects. They have been studied extensively by the famous American-Swiss astronomer Fritz Zwicky (there is a notable paper by Baade and Zwicky from 1934); Zwicky gave them their name. They have been known to have nearly uniform luminosity; this feature is easily understood from the currently favored explanation for the physics of these events: these are white dwarf stars accreting matter from a companion, going over the Chandrasekhar limit, and undergoing explosion. The best standard candles known today { also satisfying the requirement that they are bright enough so they can be observed to cosmological distances { are type Ia supernovae (SNIa). These are presumed (so, not 100% certain but very likely) to be binary systems where a white dwarf is accreting matter from a companion star, reaching the critical Chandrasekhar mass. The density gets high, the temperature gets high, and a thermonuclear flame starts. These are extremely powerful explosions seen to distant parts of the universe. Cosmology with SNIa. However, a real problem was scheduling telescopes to detect and \follow-up" SN that are discovered. Basically, if you point a telescope at a galaxy and wait for the SN to go off, you will wait an average of 500 years. There has been a program in the 1980s to do that and it discovered only one SN, and after the peak! Four crucial developments contributed to the discovery of dark energy: 1. The first major breakthrough came in the 1990s when two teams of SN researchers Super- nova Cosmology Project (SCP; led by Saul Perlmutter and organized in the late 1980s) and High-z Supernova Search Team (Highz; organized in the mid 1990s and led, at the time, by Brian Schmidt) developed an efficient approach to use world's most powerful telescopes working in concert to discover and follow up high-redshift SN, and thus complement the existing efforts at lower redshift led by the Cal´an/Tololo collaboration. These teams had been able to essentially guarantee that they would find batches of SN in each run. [For popular reviews of these exciting developments, see Bob Kirshner's book \The Extravagant Universe" and the Perlmutter-Schmidt article \Measuring Cosmology with Supernovae".] 2. The second breakthrough came in 1993 by Mark Phillips, astronomer working in Chile. He noticed that the SN luminosity { or absolute magnitude { is correlated with the decay time of SN light curve. Phillips considered the quantity ∆m15, the attenuation of the flux of SN between the light maximum and 15 days past the maximum. He found that ∆m15 is strongly correlated with the intrinsic brightness of SN; see the left panel of Fig. 1. The \Phillips relation" roughly goes as Broader is brighter: In other words, supernovae with broader light-curves have a larger intrinsic luminosity. One way to quantify this relation is to use a \stretch" factor which is a (calibration) parameter that measures width of a light curve; see the right panel of Fig. 1. By applying the correction based upon the Phillips relation, astronomers found that the intrinsic dispersion of SN, which is of order 0:5 magnitudes, can be brought down to δm 0:2 magnitudes ∼ ∼ 2 B Band -20 as measured -19 1993ApJ...413L.105P /65) -18 h 5 log( – B -17 M -16 Calan/Tololo SNe Ia -15 -20 0 20 40 60 days -20 light-curve timescale -19 “stretch-factor” corrected /65) -18 h 5 log( – -17 B M -16 -15 -20 0 20 40 60 days Kim, et al. (1997) Figure 1: Left panel: Phillips relation, from his 1993 paper. The (apparent) magnitude of type Ia supernovae is correlated with ∆m15, the decay of the light curve 15 days after the maximum. Right panel: light curves of a sample of SNIa before correction for the Phillips relation (top), and after (bottom). once we correct each SN luminosity using its stretch factor. Note that the final dispersion in magnitudes corresponds to the error in distance of ln 10 δdL=dL = δm 0:5 δm 0:1: (2) 5 ' ' The Phillips relation was the second key ingredient that enabled SNIa to achieve precision needed to probe contents of the universe accurately. 3. The third key invention was the development of techniques to correct SN magnitudes for dimming by dust, or 'extinction', out of multi-color observation of SN light. Such corrections are an important part of SN cosmology to this day. 4. Finally, the fourth and perhaps most important ingredient for the discovery of dark en- ergy was development and application of charge-coupled devices (CCDs) in observational astronomy. Both teams of SN hunters used the CCDs, which had originally been installed at telescopes at Kitt Peak and Cerro Tololo. Some of the early results came out in 1997, which paradoxically indicated that the universe is matter-dominated and consistent with being flat. However the definitive results came out in 1998 (High-z team) and 1999 (SCP, though they had results earlier) and indicated that the universe is dominated by a component with negative pressure. Observable and inferred quantities with SNIa. The astronomers use apparent magni- tudes to measure apparent (measured) brightness of an object. The apparent magnitude is given 3 44 High-Z SN Search Team 42 Supernova Cosmology Project 40 38 WM=0.3, WL=0.7 m-M (mag) 36 W W 1 M=0.3, L=0.0 always accelerates W W 34 M=1.0, L=0.0 0.5 accelerates now 1.0 decelerates in the past 0.5 0.0 (m-M) 0 ! (m-M) (mag) D -0.5 open flat -1.0 -0.5 always decelerates closed 0.01 0.10 1.00 z 0 0.5 1 1.5 2 Redshift z Figure 2: Left panel: Hubble diagram of two supernova teams indicating that distant SNIa are dimmer than expected in a matter-dominated universe. Right panel: same Hubble diagram, except with newer data, which now has been binned (grouped) in redshift for easier viewing. I also show several models to guide the eye; the model favored by the data is of course the \accelerates now, decelerated in the past" model with ΩM 1 ΩΛ 0:25.